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Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model

  • Book
  • © 2015

Overview

Authors:
  1. Takashi Suzuki

    1. Graduate School of Engineering Science, Osaka University, Toyonaka, Japan

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  • Clarifying common mathematical structures used in wide area of sciences; physics, chemistry, biology
  • Striking mathematical phenomena emerged from these structures, recognized only by these new points of view; quantized blowup mechanism, spatially homogenization, interface regularity, and so forth
  • Linking of physical principles and mathematical analysis to nonlinear non-stationary models, that is the nonlinear spectral mechanics, especially valid in the region of near from equilibrium
  • Includes supplementary material: sn.pub/extras

Part of the book series: Atlantis Studies in Mathematics for Engineering and Science (ASMES, volume 11)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Chemotaxis

    • Takashi Suzuki
    Pages 1-45

  3. Time Relaxization

    • Takashi Suzuki
    Pages 47-79

  4. Toland Duality

    • Takashi Suzuki
    Pages 81-110

  5. Phenomenology

    • Takashi Suzuki
    Pages 111-139

  6. Phase Transition

    • Takashi Suzuki
    Pages 141-157

  7. Critical Phenomena of Isolated Systems

    • Takashi Suzuki
    Pages 159-202

  8. Self-interacting Fluids

    • Takashi Suzuki
    Pages 203-245

  9. Magnetic Fields

    • Takashi Suzuki
    Pages 247-268

  10. Boltzmann-Poisson Equation

    • Takashi Suzuki
    Pages 269-296

  11. Particle Kinetics

    • Takashi Suzuki
    Pages 297-317

  12. Parabolic Equations

    • Takashi Suzuki
    Pages 319-347

  13. Gauge Fields

    • Takashi Suzuki
    Pages 349-410

  14. Higher-Dimensional Blowup

    • Takashi Suzuki
    Pages 411-422

  15. Back Matter

    Pages 423-444
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Keywords

About this book

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.  spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature.  The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

Authors and Affiliations

  • Graduate School of Engineering Science, Osaka University, Toyonaka, Japan

    Takashi Suzuki

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